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The '''trajectory''' of an object is the path it takes through space. It is often described by the [[position]] of an object as a function of time. An example is that of a cannon ball, but it applies to any path such as the [[orbit]] of a [[planet]] or a rocket in space. In [[classical mechanics]], the trajectory of a particle with mass m is described by [[Newton's Laws of Motion|Newton's second law]],

The '''trajectory''' of an object is the path it takes through space. It is often described by the [[position]] of an object as a function of time. An example is that of a cannonball, but it applies to any path such as the [[orbit]] of a [[planet]] or a rocket in space. In [[classical mechanics]], the trajectory of a particle with mass m is described by [[Newton's Laws of Motion|Newton's second law]],

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==Projectile motion==

==Projectile motion==

A useful example of trajectories is that of projectile motion, such as the motion of a cannon ball. The simplest case is that of where drag is ignored and the force of [[gravity]] on the projectile is taken to be constant. In this case, an exact solution for the trajectory may be found using the [[SUVAT equations]]. As the [[acceleration]] of the particle in the x and y directions are independent, the motion in each dimension can be considered separately. For a body with initial speed, u, fired at an angle θ above the horizontal, the x an y components of the body's [[velocity]] can be split into components: <math>u_x = v \cos{\theta}</math> and <math>u_y = u \sin{\theta}</math>. The x and y positions of the particle can be expressed as:

A useful example of trajectories is that of projectile motion, such as the motion of a cannonball. The simplest case is that of where drag is ignored and the force of [[gravity]] on the projectile is taken to be constant. In this case, an exact solution for the trajectory may be found using the [[SUVAT equations]]. As the [[acceleration]] of the particle in the x and y directions are independent, the motion in each dimension can be considered separately. For a body with initial speed, u, fired at an angle θ above the horizontal, the x an y components of the body's [[velocity]] can be split into components: <math>u_x = v \cos{\theta}</math> and <math>u_y = u \sin{\theta}</math>. The x and y positions of the particle can be expressed as:

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</math>

</math>

Hence the path followed by a body such as cannon ball is roughly [[quadratic equation|parabolic]].

Hence the path followed by a body such as cannonball is roughly [[quadratic equation|parabolic]].

===Range and Maximum Height===

===Range and Maximum Height===

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==See Also==

==See also==

* [[Classical mechanics]]

* [[Classical mechanics]]

* [[SUVAT equations]]

* [[SUVAT equations]]

==External Links==

==External links==

[http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html Trajectory at Hyperphysics]

* [http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html Trajectory at Hyperphysics]

[[Category:Physics]]

[[Category:Physics]]

[[Category:Mechanics]]

[[Category:Mechanics]]